A095323 - OEIS

%I #14 Dec 09 2015 08:27:43

%S 2,3,5,7,11,13,17,19,23,29,37,41,43,47,53,59,61,67,71,73,79,83,89,97,

%T 101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,181,193,

%U 197,199,211,227,229,233,241,257,263,269,271,277,281,283,293

%N Primes in whose binary expansion the number of 1 bits is <= 4 + number of 0 bits.

%C Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with five 1 bits and no 0 bits is the first prime excluded from this sequence. Note that 15 (1111 in binary) is not prime.

%H A. Karttunen and J. Moyer: <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%t Select[Prime[Range[100]],DigitCount[#,2,1]<(5+DigitCount[#,2,0])&] (* _Harvey P. Dale_, Dec 09 2015 *)

%o (PARI) B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;

%o for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );

%o if(b1 <= (4+b0), return(1);, return(0););};

%o forprime(x = 2, 293, if(B(x), print1(x, ", "); ); ); \\ _Washington Bomfim_, Jan 12 2011

%Y Complement of A095322 in A000040. Subset of A095285. subset: A095319. Cf. A095325.

%K nonn,base,easy

%O 1,1

%A _Antti Karttunen_, Jun 04 2004